Multilayer models for shallow two-phase debris flows with dilatancy effects

We present here a multilayer model for shallow grain-fluid mixtures with dilatancy effects. It can be seen as a generalization of the depth-averaged model presented in Bouchut et al. (2016) [6], that includes dilatancy effects by considering a two-layer model, a mixture grain-fluid layer and an upper fluid layer, to allow the exchange of fluid between them. In the present work the approximation of the mixture layer is improved including normal variations of the velocities and concentrations of the two phases thanks to the multilayer approach. In the model presented here dilatancy effects induce in particular a non-hydrostatic pressure for both phases related to the excess pore fluid pressure. Contrary to the single-layer model, the computation of this excess pore pressure entrains a serious difficulty due to the multilayer approach. We identified here one of the main numerical difficulty of solving two-phase shallow debris flows models: the strongly non-linear behaviour and abrupt changes of the excess pore fluid pressure when starting from non-equilibrium conditions. We propose a simplified approach to approximate the excess pore fluid pressure in the simple case of uniform flows in the downslope direction and quantify the error made. Our method makes it possible to introduce two or three layers in the normal directions with a reasonable approximation. Analytical solutions for uniform grain-fluid flows over inclined planes, with and without side wall friction, are calculated and compared to the proposed model. The presented model preserves the total solid granular mass as in [6]. In the numerical results, we observe that the proposed model with a two layer description of the mixture accurately represents the velocity measured at the surface of the mixture in the laboratory experiments. This is obviously poorly represented by the depth-averaged velocity in single-layer models while the other quantities (solid volume fraction, basal excess pore fluid pressure) are similar to those obtained with single-layer models. Our numerical results show a significant impact of the parameters involved in dilatancy law, in particular on the calculation of the time evolution of the excess pore fluid pressure

A weakly non-hydrostatic shallow model for dry granular flows

A non-hydrostatic depth-averaged model for dry granular flows is proposed, taking into account vertical acceleration. A variable friction coefficient based on the $\mu(I)$ rheology is considered. The model is obtained from an asymptotic analysis in a local reference system, where the non-hydrostatic contribution is supposed to be small compared to the hydrostatic one. The non-hydrostatic counterpart of the pressure may be written as the sum of two terms: one corresponding to the stress tensor and the other to the vertical acceleration. The model introduced here is weakly non-hydrostatic, in the sense that the non-hydrostatic contribution related to the stress tensor is not taken into account due to its complex implementation. A simple and efficient numerical scheme is proposed. It consists of a three-step splitting procedure, and it is based on a hydrostatic reconstruction. Two key points are: (i) the friction force has to be taken into account before solving the non-hydrostatic pressure. Otherwise, the incompressibility condition is not ensured; (ii) both the hydrostatic and the non-hydrostatic pressure are taken into account when dealing with the friction force. The model and numerical scheme are then validated based on several numerical tests, including laboratory experiments of granular collapse. The influence of non-hydrostatic terms and of the choice of the coordinate system (Cartesian or local) is analyzed. We show that non-hydrostatic models are less sensitive to the choice of the coordinate system. In general, the non-hydrostatic model introduced here much better reproduces granular collapse experiments compared to hydrostatic models. An important result is that the simulated mass profiles up to the deposit and the front velocity are greatly improved. As expected, the influence of the non-hydrostatic pressure is shown to be larger for small values of the slope

A general vertical decomposition of Euler equations: Multilayer-moment models

In this work, we present a general framework for vertical discretizations of Euler equations. It generalizes the usual moment and multilayer models and allows to obtain a family of multilayer-moment models. It considers a multilayer-type discretization where the layerwise velocity is a polynomial of arbitrary degree N on the vertical variable. The contribution of this work is twofold. First, we compare the multilayer and moment models in their usual formulation, pointing out some advantages/disadvantages of each approach. Second, a family of multilayer-moment models is proposed. As particular interesting case we shall consider a multilayer-moment model with layerwise linear horizontal velocity. Several numerical tests are presented, devoted to the comparison of multilayer and moment methods, and also showing that the proposed method with layerwise linear velocity allows us to obtain second order accuracy in the vertical direction. We show as well that the proposed approach allows to correctly represent the vertical structure of the solutions of the hydrostatic Euler equations. Moreover, the measured efficiency shows that in many situations, the proposed multilayer-moment model needs just a few layers to improve the results of the usual multilayer model with a high number of vertical layers

A general vertical decomposition of Euler equations: Multilayer-moment models

In this work, we present a general framework for vertical discretizations of Euler equations. It generalizes the usual moment and multilayer models and allows to obtain a family of multilayer-moment models. It considers a multilayer-type discretization where the layerwise velocity is a polynomial of arbitrary degree N on the vertical variable. The contribution of this work is twofold. First, we compare the multilayer and moment models in their usual formulation, pointing out some advantages/disadvantages of each approach. Second, a family of multilayer-moment models is proposed. As particular interesting case we shall consider a multilayer-moment model with layerwise linear horizontal velocity. Several numerical tests are presented, devoted to the comparison of multilayer and moment methods, and also showing that the proposed method with layerwise linear velocity allows us to obtain second order accuracy in the vertical direction. We show as well that the proposed approach allows to correctly represent the vertical structure of the solutions of the hydrostatic Euler equations. Moreover, the measured efficiency shows that in many situations, the proposed multilayer-moment model needs just a few layers to improve the results of the usual multilayer model with a high number of vertical layers.This research has been partially supported by the Spanish Government and FEDER through the research projects RTI2018-096064-B-C2(1/2) and PID2020-114688RB-I00, the Junta de Andalucía research project P18-RT-3163, the Junta de Andalucia-FEDER-University of Málaga research project UMA18-FEDERJA-16. Funding for open access charge: Universidad de Málaga / CBUA

Fluid history related to the early Eocene-middle Miocene convergent system of the Northern Apennines (Italy). Constraints from structural and isotopic studies

The late Eocene-middle Miocene erosive plate boundary between the European and the Adriatic plates is exhumed in the Northem Apennines of Italy. The fossil fault zone is 500 m thick and the outcropping portion exposes the :first 5 km of its depth. At this plate boundary basai and frontal tectonic erosion incorporated unlithified, fluid-rich sediments into the fault zone. The deformation and nature of the material along the plate boundary define a fossil subduction channel. Here we couple a detailed structural analysis of the Apennine subduction channel, focusing, in particular, on calcite veins, with a stable isotope analysis to characterize the fluid regime along an active subduction channel. The 13C and 180 composition of calcite vein and host rock samples within the fault zone indicates that there is a deep metamorphic source of fluids migrating upward along the subduction channel, in addition to locally derived fluid components. Dewatering of subducting turbidites contributes significantly only in the shallowest part of the channel. Structural observations indicate fluid flow along and across the subduction channel. At deep levels fluid flow is associated with discrete deformation events on shear faults offset by dilational jogs :filled with implosion breccias. At intennediate levels deformation is stili cyclic and associated with repeated crack-and-seal events. At the shallowest levels deformation occurred, while portions of the subducting material were stili unlithi:fied. Here the deformation was quasicontinuous, without associated vein development. Both isotope and structural analyses indicate that this erosive subduction channel behaved as a weak: fault with a vertical maximum principal stres

Flow resistance, sediment transport, and bedform development in a steep gravel-bedded river flume

Quantifying flow resistance and sediment transport rates in steep streams is important for flood and debris flow prediction, habitat restoration, and predicting how mountainous landscapes evolve. However, most studies have focused on low gradient rivers and the application of this work is uncertain for steep mountain streams where surface flows are shallow and rough, subsurface flows are not negligible, and there is form-drag from bed- and channel-forms that differs from those in low gradient rivers. To evaluate flow resistance relations and sediment transport rates for steep channel beds, experiments were conducted using a range of water discharges and sediment transport rates in a 12 m long recirculating flume with bed slopes of 10%, 20%, and 30%, and a bed of nearly uniform natural gravel. Flow resistance for planar beds and beds that developed bedforms match empirical models that account for bedload-dependent roughness. Some bedforms were atypical for natural rivers at these bed slopes, such as stepped alternate bars and upstream migrating alternate bars. Total flow resistance increased with decreasing particle submergence and energetic sediment transport and drag on bedforms. Using linear stress partitioning to calculate bed stresses due to grain resistance alone, sediment flux relations developed for lower gradient rivers perform well overall, but they overestimate fluxes at 20% and 30% gradients. Based on previous theory, mass failure of the bed, which did not occur, was predicted for the highest Shields stresses investigated at 20% and 30% bed slopes; instead a concentrated layer, four to ten particle diameters deep, of highly concentrated granular sheetflow was observed

Augmentation of WRF-Hydro to simulate overland-flow- and streamflow-generated debris flow susceptibility in burn scars

In steep wildfire-burned terrains, intense rainfall can produce large runoff that can trigger highly destructive debris flows. However, the ability to accurately characterize and forecast debris flow susceptibility in burned terrains using physics-based tools remains limited. Here, we augment the Weather Research and Forecasting Hydrological modeling system (WRF-Hydro) to simulate both overland and channelized flows and assess postfire debris flow susceptibility over a regional domain. We perform hindcast simulations using high-resolution weather-radar-derived precipitation and reanalysis data to drive non-burned baseline and burn scar sensitivity experiments. Our simulations focus on January 2021 when an atmospheric river triggered numerous debris flows within a wildfire burn scar in Big Sur – one of which destroyed California's famous Highway 1. Compared to the baseline, our burn scar simulation yields dramatic increases in total and peak discharge and shorter lags between rainfall onset and peak discharge, consistent with streamflow observations at nearby US Geological Survey (USGS) streamflow gage sites. For the 404 catchments located in the simulated burn scar area, median catchment-area-normalized peak discharge increases by ∼ 450 % compared to the baseline. Catchments with anomalously high catchment-area-normalized peak discharge correspond well with post-event field-based and remotely sensed debris flow observations. We suggest that our regional postfire debris flow susceptibility analysis demonstrates WRF-Hydro as a compelling new physics-based tool whose utility could be further extended via coupling to sediment erosion and transport models and/or ensemble-based operational weather forecasts. Given the high-fidelity performance of our augmented version of WRF-Hydro, as well as its potential usage in probabilistic hazard forecasts, we argue for its continued development and application in postfire hydrologic and natural hazard assessments.</p

Flow resistance, sediment transport, and bedform development in a steep gravel-bedded river flume

Quantifying flow resistance and sediment transport rates in steep streams is important for flood and debris flow prediction, habitat restoration, and predicting how mountainous landscapes evolve. However, most studies have focused on low gradient rivers and the application of this work is uncertain for steep mountain streams where surface flows are shallow and rough, subsurface flows are not negligible, and there is form-drag from bed- and channel-forms that differs from those in low gradient rivers. To evaluate flow resistance relations and sediment transport rates for steep channel beds, experiments were conducted using a range of water discharges and sediment transport rates in a 12 m long recirculating flume with bed slopes of 10%, 20%, and 30%, and a bed of nearly uniform natural gravel. Flow resistance for planar beds and beds that developed bedforms match empirical models that account for bedload-dependent roughness. Some bedforms were atypical for natural rivers at these bed slopes, such as stepped alternate bars and upstream migrating alternate bars. Total flow resistance increased with decreasing particle submergence and energetic sediment transport and drag on bedforms. Using linear stress partitioning to calculate bed stresses due to grain resistance alone, sediment flux relations developed for lower gradient rivers perform well overall, but they overestimate fluxes at 20% and 30% gradients. Based on previous theory, mass failure of the bed, which did not occur, was predicted for the highest Shields stresses investigated at 20% and 30% bed slopes; instead a concentrated layer, four to ten particle diameters deep, of highly concentrated granular sheetflow was observed